Critical Analysis of Corneal Cross-linking (Part-I): Formulas for Efficacy, Safety Dose, Minimum Thickness, Demarcation Line Depth and the Role of Oxygen

Purpose: To update and derive formulas for the efficacy and kinetics of corneal collagen crosslinking (CXL) including both type-I and oxygen-mediated type-II mechanisms, the role of oxygen, the initiator regeneration, safety dose, minimum corneal thickness and demarcation line depth. Study Design: Modeling the kinetics of CXL in UV light and using riboflavin as the photosensitizer. Place and Duration of Study: Taipei, Taiwan, between June, 2021 and July, 2021. Methodology: Coupled kinetic equations are derived under the quasi-steady state condition for the 2-pathway mechanisms of CXL. For type-I CXL, the riboflavin (RF) triplet state [T] may interact directly with the stroma collagen substrate [A] to form radical (R) and regenerate initiator. For type-II process, [T] interacts with oxygen to form a singlet oxygen [1O2]. Both reactive radical (R) and [1O2], can interact with the substrate [A]) for crosslinking. Based on a safety dose and a threshold dose, formulas for the minimum corneal thickness and demarcation line depth (DLD) are derived. Results: Our updated theory/modeling showed that oxygen plays a limited and transient role in the process, in consistent with that of Kamave. In contrary, Kling et al believed that type-II is the predominant mechanism, which however conflicting with the epi-on CXL results. For both type-I and type-II, a transient state conversion (crosslink) efficacy in an increasing function of light intensity (or dose), whereas, its steady state efficacy is a deceasing function of light intensity. RF depletion in type-I is compensated by the RF regeneration term (RGE) which is a decreasing function of oxygen. For the case of perfect regeneration case (or when oxygen=0), RF is a constant due to the catalytic cycle. Unlike the conventional Dresden rule of 400 um thickness, thin cornea CXL is still safe as far as the dose is under a threshold dose (E*), based on our minimum thickness formula (Z*). Our formula for thin cornea is also clinically shown by Hafez et al for ultra thin (214 nm) CXL. Conclusion: For both type-I and type-II, the transient state conversion (crosslink) efficacy in an increasing function of light intensity (or dose), whereas, its steady state efficacy is a deceasing function of light intensity. CXL for ultra thin corneas are still safe, as far as it is under a threshold dose (E*), based on our minimum thickness (Z*) formula, which has a similar tend as that of demarcation line depth (Z').

A photospheric and chromospheric activity analysis of the quiescent retrograde-planet host ν Octantis A

ABSTRACT The single-lined spectroscopic binary ν Octantis provided evidence of the first conjectured circumstellar planet demanding an orbit retrograde to the stellar orbits. The planet-like behaviour is now based on 1437 radial velocities (RVs) acquired from 2001 to 2013. ν Oct’s semimajor axis is only 2.6 au with the candidate planet orbiting $\nu ~{\rm Oct\, A}$ about mid-way between. These details seriously challenge our understanding of planet formation and our decisive modelling of orbit reconfiguration and stability scenarios. However, all non-planetary explanations are also inconsistent with numerous qualitative and quantitative tests including previous spectroscopic studies of bisectors and line-depth ratios, photometry from Hipparcos and the more recent space missions TESS and Gaia (whose increased parallax classifies $\nu ~{\rm Oct\, A}$ closer still to a subgiant, ∼K1 IV). We conducted the first large survey of $\nu ~{\rm Oct\, A}$’s chromosphere: 198 $\rm Ca\,{\small II}$ H-line and 1160 $\rm {H}\, \alpha$ indices using spectra from a previous RV campaign (2009–2013). We also acquired 135 spectra (2018–2020) primarily used for additional line-depth ratios, which are extremely sensitive to the photosphere’s temperature. We found no significant RV-correlated variability. Our line-depth ratios indicate temperature variations of only ±4 K, as achieved previously. Our atypical $\rm Ca\,{\small II}$ analysis models the indices in terms of S/N and includes covariance significantly in their errors. The $\rm {H}\, \alpha$ indices have a quasi-periodic variability that we demonstrate is due to telluric lines. Our new evidence provides further multiple arguments realistically only in favour of the planet.

Product Line Choices

Success in global markets is not only dependent on the quality and effectiveness of a single product. For many firms, even as they focus on narrow niches, the number of product variations they can cram into a narrow market space becomes a competitive advantage. How SMEs dealt with requirements for product line depth vs. breadth and, in particular, how they managed to use platforming and modularity to maximize product variations to increase the number of SKUs offered in their chosen market space. To enable such market cramming, companies have adopted extensive modularization strategies to create a maximum of product variations from a limited set of components. Platforming is another method companies use to create multiple variations from a single platform which is more efficient to produce and market. The combination of both modularization and platforming is allowing this game to be played to an even greater extent, permitting a small company to become a relative giant in a small space.

Benchmark stars, benchmark spectrographs

Context. Gaia benchmark stars are selected to be calibration stars for different spectroscopic surveys. Very high-quality and homogeneous spectroscopic data for these stars are therefore required. We collected ultrahigh-resolution ESPRESSO spectra for 30 of the 34 Gaia benchmark stars and made them public. Aims. We quantify the consistency of the results that are obtained with different high- (R ~ 115 000), and ultrahigh- (R ~ 220 000) resolution spectrographs. We also comprehensively studied the effect of using different spectral reduction products of ESPRESSO on the final spectroscopic results. Methods. We used ultrahigh- and high-resolution spectra obtained with the ESPRESSO, PEPSI, and HARPS spectrographs to measure spectral line characteristics (line depth; line width; and equivalent width, EW) and determined stellar parameters and abundances for a subset of 11 Gaia benchmark stars. We used the ARES code for automatic measurements of the spectral line parameters. Results. Our measurements reveal that the same individual spectral lines measured from adjacent 2D (spectrum in the wavelength-order space) echelle orders of ESPRESSO spectra differ slightly in line depth and line width. When a long list of spectral lines is considered, the EW measurements based on the 2D and 1D (the final spectral product) ESPRESSO spectra agree very well. The EW spectral line measurements based on the ESPRESSO, PEPSI, and HARPS spectra also agree to within a few percent. However, we note that the lines appear deeper in the ESPRESSO spectra than in PEPSI and HARPS. The stellar parameters derived from each spectrograph by combining the several available spectra agree well overall. Conclusions. We conclude that the ESPRESSO, PEPSI, and HARPS spectrographs can deliver spectroscopic results that are sufficiently consistent for most of the science cases in stellar spectroscopy. However, we found small but important differences in the performance of the three spectrographs that can be crucial for specific science cases.

RASSINE: Interactive tool for normalising stellar spectra

Aims. We provide an open-source code allowing an easy, intuitive, and robust normalisation of spectra. Methods. We developed RASSINE, a Python code for normalising merged 1D spectra through the concepts of convex hulls. The code uses six parameters that can be easily fine-tuned. The code also provides a complete user-friendly interactive interface, including graphical feedback, that helps the user to choose the parameters as easily as possible. To facilitate the normalisation even further, RASSINE can provide a first guess for the parameters that are derived directly from the merged 1D spectrum based on previously performed calibrations. Results. For HARPS spectra of the Sun that were obtained with the HELIOS solar telescope, a continuum accuracy of 0.20% on line depth can be reached after normalisation with RASSINE. This is three times better than with the commonly used method of polynomial fitting. For HARPS spectra of α Cen B, a continuum accuracy of 2.0% is reached. This rather poor accuracy is mainly due to molecular band absorption and the high density of spectral lines in the bluest part of the merged 1D spectrum. When wavelengths shorter than 4500 Å are excluded, the continuum accuracy improves by up to 1.2%. The line-depth precision on individual spectrum normalisation is estimated to be ∼0.15%, which can be reduced to the photon-noise limit (0.10%) when a time series of spectra is given as input for RASSINE. Conclusions. With a continuum accuracy higher than the polynomial fitting method and a line-depth precision compatible with photon noise, RASSINE is a tool that can find applications in numerous cases, for example stellar parameter determination, transmission spectroscopy of exoplanet atmospheres, or activity-sensitive line detection.

HDO and SO2 thermal mapping on Venus

Since January 2012, we have been monitoring the behavior of sulfur dioxide and water on Venus, using the Texas Echelon Cross-Echelle Spectrograph imaging spectrometer at the NASA InfraRed Telescope Facility (IRTF, Mauna Kea Observatory). Here, we present new data recorded in February and April 2019 in the 1345 cm−1 (7.4 μm) spectral range, where SO2, CO2, and HDO (used as a proxy for H2O) transitions were observed. The cloud top of Venus was probed at an altitude of about 64 km. As in our previous studies, the volume mixing ratio (vmr) of SO2 was estimated using the SO2/CO2 line depth ratio of weak transitions; the H2O volume mixing ratio was derived from the HDO/CO2 line depth ratio, assuming a D/H ratio of 200 times the Vienna standard mean ocean water. As reported in our previous analyses, the SO2 mixing ratio shows strong variations with time and also over the disk, showing evidence for the formation of SO2 plumes with a lifetime of a few hours; in contrast, the H2O abundance is remarkably uniform over the disk and shows moderate variations as a function of time. We have used the 2019 data in addition to our previous dataset to study the long-term variations of SO2 and H2O. The data reveal a long-term anti-correlation with a correlation coefficient of −0.80; this coefficient becomes −0.90 if the analysis is restricted to the 2014–2019 time period. The statistical analysis of the SO2 plumes as a function of local time confirms our previous result with a minimum around 10:00 and two maxima near the terminators. The dependence of the SO2 vmr with respect to local time shows a higher abundance at the evening terminator with respect to the morning. The dependence of the SO2 vmr with respect to longitude exhibits a broad maximum at 120–200° east longitudes, near the region of Aphrodite Terra. However, this trend has not been observed by other measurements and has yet to be confirmed.